Congruent shapes or congruent figures are shapes that are exactly the same.
Understanding Congruent Shapes
When geometric shapes are described as congruent, it signifies that they are perfect duplicates of each other. They have the identical size and the identical form. If you could pick one up and place it on top of the other, they would match up perfectly, covering each other completely.
Defining Congruence
Based on the provided reference, the definition of congruent shapes includes these key points:
- The corresponding sides are the same. This means if Shape A has a side of length 5 cm, the corresponding side in the congruent Shape B will also have a length of 5 cm. This holds true for all pairs of corresponding sides.
- The corresponding angles are the same. Similarly, if Shape A has an angle measuring 60 degrees, the corresponding angle in the congruent Shape B will also measure 60 degrees. This applies to all pairs of corresponding angles.
How to Check for Congruence
As the reference highlights, to determine if two shapes are congruent, you need to verify their corresponding parts.
To do this, we need to check:
- All the corresponding angles: Match up the angles of the two shapes and ensure each pair has an equal measure.
- All the corresponding sides: Match up the sides of the two shapes and ensure each pair has an equal length.
If every single corresponding side and every single corresponding angle is equal between two shapes, then and only then are they congruent.
Practical Example: Congruent Squares
Consider two squares. For them to be congruent:
- All four sides of the first square must be exactly the same length as all four sides of the second square.
- All four angles of the first square (which are 90 degrees) must be the same as all four angles of the second square (which are also 90 degrees).
If one square has sides of 5 cm and another has sides of 5.1 cm, they are not congruent, even though their angles are the same. Similarly, two rectangles with sides 4x6 cm and 4x6 cm are congruent, but a 4x6 cm rectangle is not congruent to a 3x8 cm rectangle.
Congruent vs. Similar Shapes
It's helpful to contrast congruent shapes with similar shapes.
| Feature | Congruent Shapes | Similar Shapes |
|---|---|---|
| Size | Exactly the same | Can be different (scaled) |
| Shape | Exactly the same | Exactly the same |
| Side Lengths | Corresponding sides are equal | Corresponding sides are proportional |
| Angle Measures | Corresponding angles are equal | Corresponding angles are equal |
Congruent shapes are essentially similar shapes with a scale factor of 1.
In summary, congruent shapes are identical copies, possessing the same measurements for all corresponding sides and angles.
